Canon 70-300 USM IS extremely unsharp

No much information here so I'll take a stab in the dark. The subject is so small it is unlikely the camera (auto AF selection) had the smarts to know what you wanted in focus. You need to take control of focus and select what you want to be sharp (manually select the AF point and place it on the bird). If you did place the active AF point on the bird, then your lens is suffering from front focus and needs calibration at Canon Service. No biggie. They'll fix it in 10 days or so including shipping and you'll be in like friggen flint.

Of course AF point was in dead center of the bird

I also think you might have experienced a focus issue, and not a lens failure. I never had a sharpness issue with my old 70-300 lens. This shot was made with the DO version of the 70-300, but it has always had about the same sharpness as my previous 70-300, and the size of this bird serves to make the point about the camera having a sure target area to focus on. Barring that, you might need to have your camera and 70-300 tweaked by the folks at Canon service to nail correct focus spot on.

So I should send them both?
This focus is the camera problem?
Another thing is that the service is in another city and it can take long time.
And I would be without my lovely camera...

Maybe it's just because the AF accuracy is not as great as advertised? I do a lot of critical focusing and I notice that the prosumer *0D dSLRs are much worse than the 5D, which in turn is probably not as good as the 1D cameras. Also keep in mind that the AF points in reality are three times as large as the AF selectors in the viewfinder, so if there is focus archieved anywhere in this area, the camera signals you that AF is spot-on.

1. Compare AF to MF.
2. If you have a camera with MA, check that as well.

Happy shooting,
Yakim.

As the old maxim goes," if your subject isn't big enough, you aren't close enough." Without knowing your shooting technique, it's unfair to blame the lens. That is one small pheasant in a large area. Try using a tripod and focusing on something larger that you can test the lens on. Try shooting some larger birds under good light - A frame-filling swan or a canada goose ought to have plenty of detail in sharp focus from 10- 20 feet away with such a lens.

In your first image the focus point is clearly a couple of feet in front of the bird where the grass borders the dirt. The depth of field appears to be a foot or less.

You are too far away for it to be very good even in sharp focus. Try to get closer or think about a longer lens if wildlife photography is of high interest to you.

I agree with Mark O'Brien and most of what else is written here....
What I see here is not a reason to suspect the lens and start shipping things off to Canon to be checked. I think some easy tests with frame-filling subjects on a tripod at 300mm would be the next logical step.
While I agree (and Canon plainly states) that the auto-focus point coverage is actually larger than the black squares in your viewfinder, I'm not sure where Bueh got the information that "...the AF points in reality are three times as large as the AF selectors in the viewfinder". I don't think that's entirely correct...
Just try some 300mm tripod testing on a subject that fills the whole frame and see what happens.
John